Hourly Prediction

Using the event scale model a call rate $z_i$ of the next hour $i$ is expressed this way

$$z_i=z_{i-1}\ s_i.$$ (118)

Here $z_{i-1}$ is the present call rate and $s_i$ is a scale of the next hour $i$ The hourly scales $s_i$ may differ depending on the impact of SE felt at the day $i$: working, weekend, Christmas, marketing messages e.t.c.

$$s_i=\frac {z_{p(i)}}{z_{p(i-1)}}.$$ (119)

Her $p(i)$ is a subscript of the hour preceding the next one and $p(i-1)$ is a subscript of the hour preceding present one. Meaning of the term "preceding" is illustrated by following examples.